High School Calculus Velocity question

1. The problem statement, all variables and given/known data
If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

2. Relevant equations
Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for earth -4.9t^2 -22t +443.

3. The attempt at a solution
To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

1. The problem statement, all variables and given/known data
If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

2. Relevant equations
Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for earth -4.9t^2 -22t +443.

3. The attempt at a solution
To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

1. The problem statement, all variables and given/known data
If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact?

2. Relevant equations
Since the ball is being thrown down with a velocity of 22 m/s I plug that into the gravitational constant equation for earth -4.9t^2 -22t +443.

3. The attempt at a solution
To get when the ball hits the ground I set -4.9t^2 -22t +443=0. Solving for t I get about ~7.5. To get the speed at impact I took the second derivative which is -9.8t -22. Plugging in t into this equation I get |-9.8(7.5) -22| for 95.5 m/s for the speed at impact. Was this problem handled in the correct fashion?

-9.8t-22 is not the second derivative; it's the first derivative of the position function, -4.9t2-22t+443 = 0.